Demulsification-dehydration method by using chaotic-frequency pulse group electric field

ABSTRACT

A demulsification-dehydration method by using a chaotic-frequency pulse group electric field, including: subjecting a waste oil emulsion to the chaotic-frequency pulse group electric field for demulsification and dehydration. The chaotic-frequency pulse group electric field includes a plurality of pulse electric field groups varying in pulse frequency. The pulse frequency of each pulse electric field group varies chaotically within a preset range. Each pulse electric field group includes a plurality of pulses of equal frequency, duty cycle and electric field intensity.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority from Chinese Patent Application No. 202110665685.1, filed on Jun. 16, 2021. The content of the aforementioned applications, including any intervening amendments thereto, is incorporated herein by reference in its entirety.

TECHNICAL FIELD

The present application relates to a physical or chemical method for electrically separating droplets, and more particularly to a demulsification-dehydration method by using a chaotic-frequency pulse group electric field.

BACKGROUND

The waste lubricating oil, known as industrial waste oil, is an industrial hazardous waste formed by gradual aging and deterioration of lubricating oil in use caused by solid impurity and water pollution under the exposure to physical, chemical or human factors. The waste lubricating oil has complex chemical composition, and contains a large number of harmful heavy metals and sulfur, phosphorus and chlorine-containing toxic compounds. The waste lubricating oil should be treated properly, otherwise, it will threaten the ecological environment. Purifying the waste lubricating oil to restore its base oil properties can achieve the recycle of lubricating oil, which not only protects the environment, but also facilitates alleviating the energy resource shortage.

At present, the demulsification and dehydration of the waste lubricating oil is performed commonly by sedimentation, chemical, centrifugal, electric field and vacuum methods, but these approaches fail to achieve the high efficiency and low energy consumption at the same time. The emerging pulse electric field demulsification method has simple device structure, high efficiency and low energy consumption, which is suitable for the treatment of waste lubricating oil. It has been demonstrated that under the action of the pulse electric field, droplets in oil undergo vibration and deformation, and thus the strength of an oil-water interfacial film is greatly weakened and the droplets are more prone to agglomeration. Additionally, under the optimal electric field frequency, the droplets will resonate, namely the deformation amplitude reaches the maximum without breaking, which increases the collision probability between droplets and realizes the efficient agglomeration and demulsification of the waste lubricating oil.

Nevertheless, the pulse electric field used for demulsification and dehydration of the waste lubricating oil is usually a constant-frequency periodic pulse, which can only make droplets of single particle size in the oil resonate. For an oil-water system with constantly-changing particle size under the action an electric field, it fails to reach an optimal resonance frequency for all droplets, lowering the demulsification and dehydration efficiency. Chinese patent application publication No. 111773769 A discloses a demulsification method using a chaotic-frequency pulse electric field, in which the waste oil emulsion is subjected to a pulse electric field with constantly-changing frequency. This method enables the full coverage of resonant frequencies of emulsified droplets, and the chaotic-frequency pulse electric field with constant amplitude and equal pulse width can also prevent adverse effects brought by the uncertainty of the electric field amplitude and pulse width. Notwithstanding, this common chaotic-frequency pulse may cause the droplets to produce unsteady vibration, and the stable response under the resonant frequency is insufficient, failing to achieve the desired resonance state and make full use of the pulse electric field.

SUMMARY

In order to overcome the problems in prior art, the present disclosure provides a demulsification-dehydration method by using a chaotic-frequency pulse group electric field to enable the sufficient stable response of droplets at a resonant frequency during the demulsification. A pulse frequency of the electric field provided herein can cover resonance frequencies of all droplets in the waste oil, and also ensure the steady-state response of droplets, allowing for improved demulsification and dehydration efficiency.

Technical solutions of the disclosure are described as follows.

A demulsification-dehydration method by using a chaotic-frequency pulse group electric field, comprising:

applying the chaotic-frequency pulse group electric field to a waste oil emulsion for demulsification and dehydration;

wherein the chaotic-frequency pulse group electric field comprises a plurality of pulse electric field groups varying in pulse frequency; a pulse frequency of each of the plurality of pulse electric field groups experiences a chaotic change within a preset range; and each of the plurality of pulse electric field groups comprises a plurality of pulses of equal frequency, duty cycle and electric field intensity.

In some embodiments, a variation of the pulse frequency of each of the plurality of pulse electric field groups is determined by equations expressed as:

$\omega_{m{ax}} = \sqrt{\frac{3.4152\gamma}{R_{min}^{3}\rho}}$ $\omega_{min} = \sqrt{\frac{3.4152\gamma}{R_{m{ax}}^{3}\rho}}$ ${\omega_{n} = \frac{\omega_{m{ax}}\omega_{min}}{{\left( {c_{n} + 1} \right){\left( {\omega_{m{ax}} - \omega_{min}} \right)/2}} + \omega_{min}}},{n = 1},2,{\ldots{and}}$ c_(n + 1) = 1 − 2c_(n)², n = 1, 2, …(−1 < c₁ < 1);

wherein ω_(max) is a maximum pulse angular frequency; ω_(min) is a minimum pulse angular frequency; ρ is droplet density; R_(max) is a particle size of a largest droplet in the waste oil emulsion; R_(min) is a particle size of a smallest droplet in the waste oil emulsion; γ is an oil-water interfacial tension; ω_(n) is a pulse angular frequency of a n^(th) pulse electric field group; and c_(n), is a value of n^(th) iteration of logistic map.

In some embodiments, the number of the plurality of pulses in each of the plurality of pulse electric field groups is determined by equations expressed as:

${\frac{d^{2}\chi}{{dt}^{2}} + {A{\varphi(\chi)}\frac{d\chi}{dt}} + {{Bf}(\chi)}} = {{{Gq}(t)}{e(\chi)}}$ $A = \frac{4\mu}{R^{2}\rho}$ $B = {\frac{8\gamma}{R^{3}\rho}{and}}$ ${G = \frac{4\varepsilon_{0}\varepsilon_{2}E^{2}}{R^{2}\rho}};$

wherein A is a resistance constant; B is an interfacial restoring force constant; G is an electric field excitation force constant; μ is a dynamic viscosity; ϵ₀ is a vacuum dielectric constant; ϵ₂ is a relative dielectric constant; E is an electric field intensity; γ is an oil-water interfacial tension; R is an initial droplet radius; ρ is a droplet density; χ is a droplet amplitude; q(t) is an electric field signal function, and expressed as

${{q(t)} = {\frac{1}{2} + {\frac{2}{\pi}\left( {{\sin\omega t} + {\frac{1}{3}\sin 3\omega t} + {\frac{1}{5}\sin 5\omega t} + \cdots} \right)}}};$

φ(χ) is a resistance nonlinear function; ƒ (χ) is an interfacial restoring force nonlinear function; e(χ) is an electric field excitation force nonlinear function; φ(χ)=0.92-2.1χ+1.17χ²; ƒ(χ)=0.25χ−0.06χ² ; e(χ)=1.47−0.83χ+0.2χ²; ω is an electric field angular frequency; and t is an electric field action time.

In some embodiments, wherein an electric field output sequence of the chaotic-frequency pulse group electric field is determined by an equation expressed as:

${{E(t)} = {E\left( {\frac{1}{2} + {\frac{2}{\pi}\left( {{\sin\left( {\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)} \right)} + {\frac{1}{3}{\sin\left( {3{\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)}} \right)}} + {\frac{1}{5}{\sin\left( {5{\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)}} \right)}} + \cdots} \right)}} \right)}},{n = 1},2,3,{\cdots;}$

wherein ω_(i), is an electric field angular frequency of an i^(th) pulse electric field group; and t is an electric field action time.

In some embodiments, in each of the plurality of pulse electric field groups, the plurality of pulses have a duty cycle of 0.5 and an electric field intensity of 100-500 kV/m.

In some embodiments, the demulsification-dehydration method further comprises:

before the chaotic-frequency pulse group electric field is applied to the waste oil emulsion, controlling the waste oil emulsion to 40-50° C.;

wherein the waste oil emulsion comprises 10-30% by weight of water, and has a kinematic viscosity of less than 65 mm²/s at 40° C.

Compared to the prior art, this application has the following beneficial effects.

(1) Regarding the demulsification-dehydration method provided herein, the chaotic-frequency pulse group electric field excites a droplet vibration in waste oil. Compared with the existing method using frequency pulse electric field, the chaotic-frequency pulse group electric field has the following characteristics. (a) Each pulse electric field group includes multiple pulses of equal frequency, duty cycle and electric field intensity. (b) The pulse frequency varies chaotically between the pulse electric field groups, i.e., the pulse frequency varies within the preset range but never repeats. The pulse frequency of the chaotic-frequency pulse group electric field is chaotic between the pulse electric field groups but constant within each pulse electric field group, with both chaotic and periodic characteristics, which can full cover a resonant frequency of a droplet electric field, and can make droplets vibrate at each pulse frequency to reach a steady state. Therefore, all droplets in the waste oil can respond effectively at their own resonant frequency and reach the resonant amplitude, effectively enhancing an agglomeration and demulsification ability of the chaotic-frequency pulse group electric field.

(2) Regarding the demulsification-dehydration method provided herein, the duty cycle is 0.5, which can avoid too small a duty cycle leading to insufficient droplet deformation and affecting a demulsification efficiency, and prevent unnecessary energy consumption caused by too large a duty cycle.

(3) Regarding the demulsification-dehydration method provided herein, each pulse electric field group consists of multiple pulses with equal frequency, duty cycle and electric field intensity to ensure the steady-state response of the droplet. The duty cycle and a frequency determination algorithm are adjusted. A pulse width is controlled by the frequency. An electric field confirmation function is adjusted. The frequency is subjected to reciprocating iteration between the resonant frequencies of each droplet, varying constantly, and generally responding to an optimal demulsification frequency for all droplets. Compared with the existing method using frequency pulse electric field, the demulsification-dehydration method provided herein has better effect and efficiency.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically depicts a chaotic-frequency pulse group electric field according to an embodiment of the present disclosure;

FIG. 2 is a frequency spectrum of a chaotic-frequency pulse group according to an embodiment of the present disclosure;

FIG. 3 schematically depicts a vibration response of a droplet at different initial values of vibration according to an embodiment of the present disclosure;

FIG. 4 schematically depicts a signal of the chaotic-frequency pulse group electric field according to an embodiment of the present disclosure;

FIG. 5 schematically depicts a vibration response of a droplet in the chaotic-frequency pulse group electric field according to an embodiment of the present disclosure; and

FIG. 6 shows comparison of vibration amplitudes of the droplet in different electric fields.

DETAILED DESCRIPTION OF EMBODIMENTS

The disclosure will be described in detail below with reference to the accompanying drawings and embodiments.

In an embodiment of a demulsification-dehydration method by using a chaotic-frequency pulse group electric field, a waste oil emulsion is subjected to pretreatment, where the waste oil emulsion includes 10-30% by weight of water, and has a kinematic viscosity of less than 65 mm²/s at 40° C. The waste oil emulsion is filtered to remove mechanical impurities, and then enters a heat exchanger to control the waste oil emulsion to 40-50° C. Further, the waste oil emulsion is subjected to demulsification and dehydration after entering an electric field demulsifier followed by an oil storage device.

Referring to FIG. 1, the electric field demulsifier applies the chaotic-frequency pulse group electric field to the waste oil emulsion for demulsification and dehydration. The chaotic-frequency pulse group electric field includes multiple pulse electric field groups varying in pulse frequency. The pulse electric field groups are applied to the waste oil emulsion in time sequence. A pulse frequency of each pulse electric field group experiences a chaotic change within a preset range and never repeat. Each pulse electric field group includes multiple pulses of equal frequency, duty cycle and electric field intensity. The pulses are applied to the waste oil emulsion in time sequence.

A variation of the pulse frequency of each pulse electric field group is determined by equations expressed as:

$\omega_{m{ax}} = \sqrt{\frac{3.4152\gamma}{R_{min}^{3}\rho}}$ $\omega_{min} = \sqrt{\frac{3.4152\gamma}{R_{m{ax}}^{3}\rho}}$ ${\omega_{n} = \frac{\omega_{m{ax}}\omega_{min}}{{\left( {c_{n} + 1} \right){\left( {\omega_{m{ax}} - \omega_{min}} \right)/2}} + \omega_{min}}},{n = 1},2,\ldots$ c_(n + 1) = 1 − 2c_(n)², n = 1, 2, …(−1 < c₁ < 1);

where ω_(max) is a maximum pulse angular frequency; ω_(min) is a minimum pulse angular frequency; ρ is droplet density; R_(max) is a particle size of a largest droplet in the waste oil emulsion; R_(min) is a particle size of a smallest droplet in the waste oil emulsion; γ is an oil-water interfacial tension; ω_(n) is a pulse angular frequency of a n^(th) pulse electric field group; and c_(n) is a value of n^(th) iteration of logistic map.

The number of the multiple pulses in each pulse electric field group is determined by equations expressed as:

${\frac{d^{2}\chi}{{dt}^{2}} + {A{\varphi(\chi)}\frac{d\chi}{dt}} + {{Bf}(\chi)}} = {{{Gq}(t)}{e(\chi)}}$ $A = \frac{4\mu}{R^{2}\rho}$ $B = \frac{8\gamma}{R^{3}\rho}$ ${G = \frac{4\varepsilon_{0}\varepsilon_{2}E^{2}}{R^{2}\rho}};$

where A is a resistance constant; B is an interfacial restoring force constant; G is an electric field excitation force constant; μ is a dynamic viscosity; Ε₀ is a vacuum dielectric constant; ϵ₂ is a relative dielectric constant; E is an electric field intensity; γ is an oil-water interfacial tension; R is an initial droplet radius; ρ is a droplet density; χ is a droplet amplitude; q(t) is an electric field signal function, and expressed as

${{q(t)} = {\frac{1}{2} + {\frac{2}{\pi}\left( {{\sin\omega t} + {\frac{1}{3}\sin 3\omega t} + {\frac{1}{5}\sin 5\omega t} + \cdots} \right)}}};$

φ(χ) is a resistance nonlinear function; ƒ (χ) is an interfacial restoring force nonlinear function; e(χ) is an electric field excitation force nonlinear function; φ(χ)=0.92−2.1χ+1.17χ²; ƒ(χ)=0.25χ−0.06χ² ; e(χ)=1.47−0.83χ+0.2χ²; ω is an electric field angular frequency; and t is an electric field action time.

An electric field output sequence of the chaotic-frequency pulse group electric field is determined by an equation expressed as:

${{E(t)} = {E\left( {\frac{1}{2} + {\frac{2}{\pi}\left( {{\sin\left( {\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)} \right)} + {\frac{1}{3}{\sin\left( {3{\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)}} \right)}} + {\frac{1}{5}{\sin\left( {5{\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)}} \right)}} + \cdots} \right)}} \right)}},{n = 1},2,3,{\cdots;}$

where ω_(i), is an electric field angular frequency of an pulse electric field group; and t is an electric field action time.

In each pulse electric field group, the pulses have a duty cycle of 0.5 and an electric field intensity of 100-500 kV/m.

Provide below is an example.

Physical parameters of a oil-water system measured by test instruments are shown in Table 1.

TABLE 1 Physical parameters of waste oil emulsion Density Dynamic Relative Interfacial Particle Vacuum ρ viscosity μ dielectric tension γ size R dielectric (kg/m³) (Pa · s) constant ∈₂ (N/m) (m) constant ∈₀ Droplet 998 0.98 × 10⁻³ 80 19 × 10⁻³ R_(max) = 2 × 10⁻³ 8.854 × 10⁻¹² Oil 922 60.3 × 10⁻³ 4.6 R_(min) = 0.3 × 10⁻³

-   -   (1) For determining a frequency range ω_(max) and ω_(min), the         above-mentioned physical parameters are input into a frequency         calculation equation, expressed as follows:

${\omega_{m{ax}} = {\sqrt{\frac{3.4152\gamma}{R_{min}^{2}\rho}} = {1187.53{rad}/s}}},$ $\omega_{min} = {\sqrt{\frac{3.4152\gamma}{R_{m{ax}}^{3}\rho}} = {68.99{rad}/{s.}}}$

Therefore, the frequency range of the chaotic-frequency pulse group electric field ωε(ω_(min),ω_(max))=(68.99,1187.53)rad/s

(2) For determining a chaos iteration of the pulse frequency between the pulse pulse frequency groups, an initial iteration value is set to c₁=0.35. The ω_(max) and ω_(min) are plugged into a frequency chaos iteration equation, expressed as follows:

${\omega_{n} = \frac{\omega_{m{ax}}\omega_{min}}{{\left( {c_{n} + 1} \right){\left( {\omega_{m{ax}} - \omega_{min}} \right)/2}} + \omega_{min}}},{n = 1},2,{\ldots.}$

A frequency spectrum of the chaotic-frequency pulse group is shown in FIG. 2. (3) For determining the number of the pulses in each electric field groups, an electric field intensity is set as E=2×10⁵ V/m, initial values of vibration are 0.001, 0.1 and 0.2. A nonlinear vibration equation of the droplet is solved to obtain a vibration response of a droplet having the particle size of R_(max), shown in FIG. 3.

The number of vibration periods where the droplet is stabilized by periodic vibration is the number of the pulses. According to the vibration response, droplet completely stabilizes after the third vibration period, such that the number of the pulses k is 3.

(4) Since the variation and the number of pulses are determined, an electric field output sequence of the chaotic-frequency pulse group electric field is determined by an equation expressed as:

${{E(t)} = {E\left( {\frac{1}{2} + {\frac{2}{\pi}\left( {{\sin\left( {\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)} \right)} + {\frac{1}{3}{\sin\left( {3{\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)}} \right)}} + {\frac{1}{5}{\sin\left( {5{\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)}} \right)}} + \cdots} \right)}} \right)}},{n = 1},2,3,\cdots,$

results are shown in FIG. 4.

(5) The electric field output sequence is stored in a pulse power supply by programming. A positive pole of the pulse power supply is connected to a positive interface of an electric dehydration device, and a negative pole of the pulse power supply is grounded, such that the waste oil emulsion can be demulsified and dehydrated through an electric field method.

In this example, the chaotic-frequency pulse group electric field has chaotic and periodic characteristics, which overcomes problems that a constant-frequency pulse electric field fails to cover all droplet resonance frequencies in oil emulsion and a pulse electric field with variable frequency fails to satisfy a steady state response, maximizing a demulsification and dehydration efficiency of pulse electric field.

Referring to FIG. 5, the vibration response of a droplet with particle size R=1.8×10⁻³ m at the chaotic-frequency pulse group electric field is shown. Obviously, there are a chaotic vibration response and a periodic vibration response of the droplet, which have a high vibration amplitude, satisfying an expected vibration result.

Referring to FIG. 6, the constant-frequency pulse electric field plays a good resonance effect only for droplets in a very small particle size range, and a vibration amplitude of the constant-frequency pulse electric field is slightly higher than a chaotic-frequency pulse electric field and the chaotic-frequency pulse group electric field. Nevertheless, the chaotic-frequency pulse electric field and the chaotic-frequency pulse group electric field enable all droplets having a high vibration amplitude, which is better than the constant-frequency pulse electric field. In addition, the vibration amplitude of the droplet in the chaotic-frequency pulse group electric field is higher than that in the chaotic-frequency pulse electric field. In consequence, the chaotic-frequency pulse group electric field has a better vibratory agglomeration effect.

Described above are only some embodiments of the present disclosure, which are not intended to limit the disclosure. Any modifications and replacement made by those of ordinary skilled in the art without departing from the spirit of the disclosure should fall within the scope of the disclosure defined by the appended claims. 

What is claimed is:
 1. A demulsification-dehydration method by using a chaotic-frequency pulse group electric field, comprising: applying the chaotic-frequency pulse group electric field to a waste oil emulsion for demulsification and dehydration; wherein the chaotic-frequency pulse group electric field comprises a plurality of pulse electric field groups varying in pulse frequency; a pulse frequency of each of the plurality of pulse electric field groups experiences a chaotic change within a preset range; and each of the plurality of pulse electric field groups comprises a plurality of pulses of equal frequency, duty cycle and electric field intensity.
 2. The demulsification-dehydration method of claim 1, wherein a variation of the pulse frequency of each of the plurality of pulse electric field groups is determined by equations expressed as: $\omega_{m{ax}} = \sqrt{\frac{3.4152\gamma}{R_{min}^{3}\rho}}$ $\omega_{min} = \sqrt{\frac{3.4152\gamma}{R_{m{ax}}^{3}\rho}}$ ${\omega_{n} = \frac{\omega_{m{ax}}\omega_{min}}{{\left( {c_{n} + 1} \right){\left( {\omega_{m{ax}} - \omega_{min}} \right)/2}} + \omega_{min}}},{n = 1},2,{\ldots{and}}$ c_(n + 1) = 1 − 2c_(n)², n = 1, 2, …(−1 < c₁ < 1); wherein ω_(max) is a maximum pulse angular frequency; ω_(min) is a minimum pulse angular frequency; ρ is droplet density; R_(max) is a particle size of a largest droplet in the waste oil emulsion; R_(min) is a particle size of a smallest droplet in the waste oil emulsion; γ is an oil-water interfacial tension; ω_(n) is a pulse angular frequency of a n^(th) pulse electric field group; and c_(n) is a value of n^(th) iteration of logistic map.
 3. The demulsification-dehydration method of claim 1, wherein the number of the plurality of pulses in each of the plurality of pulse electric field groups is determined by equations expressed as: ${\frac{d^{2}\chi}{{dt}^{2}} + {A{\varphi(\chi)}\frac{d\chi}{dt}} + {{Bf}(\chi)}} = {{{Gq}(t)}{e(\chi)}}$ $A = \frac{4\mu}{R^{2}\rho}$ $B = {\frac{8\gamma}{R^{3}\rho}{and}}$ ${G = \frac{4\varepsilon_{0}\varepsilon_{2}E^{2}}{R^{2}\rho}};$ wherein A is a resistance constant; B is an interfacial restoring force constant; G is an electric field excitation force constant; μ is a dynamic viscosity; ϵ₀ is a vacuum dielectric constant; ϵ₂ is a relative dielectric constant; E is an electric field intensity; γ is an oil-water interfacial tension; R is an initial droplet radius; ρ is a droplet density; χ is a droplet amplitude; q(t) is an electric field signal function, and expressed as ${{q(t)} = {\frac{1}{2} + {\frac{2}{\pi}\left( {{\sin\omega t} + {\frac{1}{3}\sin 3\omega t} + {\frac{1}{5}\sin 5\omega t} + \cdots} \right)}}};$ φ(χ) is a resistance nonlinear function; ƒ (χ) is an interfacial restoring force nonlinear function; e(χ) is an electric field excitation force nonlinear function; φ(χ)=0.92−2.1χ+1.17χ²; ƒ(χ)=0.25χ−0.06χ² ; e(χ)=1.47−0.83χ+0.2χ² ; ω is an electric field angular frequency; and t is an electric field action time.
 4. The demulsification-dehydration method of claim 1, wherein an electric field output sequence of the chaotic-frequency pulse group electric field is determined by an equation expressed as: ${{E(t)} = {E\left( {\frac{1}{2} + {\frac{2}{\pi}\left( {{\sin\left( {\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)} \right)} + {\frac{1}{3}{\sin\left( {3{\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)}} \right)}} + {\frac{1}{5}{\sin\left( {5{\omega_{i}\left( {t - {\sum\limits_{i = 1}^{n - 1}{k\frac{2\pi}{\omega_{i}}}}} \right)}} \right)}} + \cdots} \right)}} \right)}},{n = 1},2,3,{\cdots;}$ wherein ω_(i) is an electric field angular frequency of an i^(th) pulse electric field group; and t is an electric field action time.
 5. The demulsification-dehydration method of claim 1, wherein in each of the plurality of pulse electric field groups, the plurality of pulses have a duty cycle of 0.5 and an electric field intensity of 100-500 kV/m.
 6. The demulsification-dehydration method of claim 1, further comprising: before the chaotic-frequency pulse group electric field is applied to the waste oil emulsion, controlling the waste oil emulsion to 40-50° C.; wherein the waste oil emulsion comprises 10-30% by weight of water, and has a kinematic viscosity of less than 65 mm²/s at 40° C. 